# A vector is rotated by a small angle radians    to get a new vector .In that case    is : Option 1) Option 2) Option 3) Option 4)

As we discussed in

Triangle law of vector Addition -

If two vector are represented by both magnitude and direction by two sides of triangle taken in same order then their resultant is represented by 3rd side of triangle.

- wherein

Represents triangle law of vector Addition

By Triangle Rule

$\vec{A}+\vec{C}= \vec{B}$

$\vec{B}-\vec{A}= \vec{C}$

$\left |\vec{B}-\vec{A} \right |=\left | \vec{C} \right |$ $=\left | \vec{B} \right |\sin \Theta (\because \Delta \Theta < < 1)$

$\left | \vec{B}-\vec{A} \right |=\left | \vec{B}\right | \Delta\Theta\ \; (\because sin\Delta \Theta =\Delta \Theta)$

Again $\left | \vec{B}\right |cos\Delta \Theta =\left | \vec{A}\right |$

$\left | \vec{B}\right | =\left | \vec{A}\right |$             $(\because cos\Delta \Theta \simeq 1)$

So $\left | \vec{B-A}\right | =\left | \vec{B}\right |\Delta \Theta =\left | \vec{A}\right |.\Delta \Theta$

Option 1)

Incorrect

Option 2)

Incorrect

Option 3)

Correct

Option 4)

Incorrect

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